Mathematics Seminar
Speaker: Jayakumar Ravindran, IMSc
Date: Wednesday, 07 August 2024
Time: 3:30 PM
Venue: Seminar Hall
Boundedness of Left Regular Representations in the Two-Sided GJS Construction
Jayakumar Ravindran
Institute of Mathematical Sciences, Chennai.
07-08-24

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Abstract

In this talk, we will explore a crucial aspect of the two-sided Guionnet-Jones-Shlyakhtenko (GJS) construction: the boundedness of left regular representations. Starting with an irreducible subfactor planar algebra P, we will examine the construction of two families of unital, associative *-algebras, A^k_G and A^k_F, and their associated Hilbert space completion H^k. We will focus on demonstrating that the left-regular representation λ(·) of A^k_F on itself extends to a bounded map on H^k. This result is fundamental to defining the von Neumann algebra M_k as λ(A^k_F)''.